Maximum entropy-based stochastic micromechanical model for a two-phase composite considering the inter-particle interaction effect

A maximum entropy-based stochastic micromechanical framework considering the inter-particle interaction effect is proposed to characterize the probabilistic behavior of the effective properties of two-phase composite materials. Based on our previous work, the deterministic micromechanical model of the two-phase composites is derived by introducing the strain concentration tensors considering the inter-particle interaction effect. By modeling the volume fractions and properties of constituents as stochastic, we extend the deterministic framework to stochastics, to incorporate the inherent randomness of effective properties among different specimens. A distribution-free method is employed to get the unbiased probability density function based on the maximum entropy principle. Further, the normalization procedures are utilized to make the probability density functions more stable. Numerical examples including limited experimental validations, comparisons with existing micromechanical models, commonly used probability density functions and the direct Monte Carlo simulations indicate that the proposed models provide an accurate and computationally efficient framework in characterizing the effective properties of two-phase composites.